Hossenfelder. on the Problem of Measuring Happiness

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Interdisciplinary Description of Complex Systems11(3), 289-301, 2013

*Corresponding author, : [email protected]; +46 8 5537 8717;*NORDITA, Roslagstullsbacken 23, 106 91 Stockholm, Sweden*

ON THE PROBLEM OF MEASURING HAPPINESS

Sabine Hossenfelder*

NORDITAStockholm, Sweden

DOI: 10.7906/indecs.11.3.2Regular article

Received:24 March 2013.Accepted: 28 June 2013.

ABSTRACT

The question of how to measure and aggregate happiness is more than a century old. In recent years, itsrelevance has risen due to efforts to replace the GDP with an index more indicative of well-being,though such efforts are fraught with serious conceptual problems. After briefly recalling these problems,we suggest to address them by using, instead of the common ordinal utility, an alternative quantity thatis maximized in economic transactions. This quantity counts the number of future possibilities acommodity opens. The big advantage of this approach is that, in principle, the number of possibilities is

an objective measure which allows for intra- and interpersonal comparison. We lay out the frameworkof the model and then discuss its relevance for social welfare. While we do here not explicitly compute ameasure supplementing the GDP, we sketch how this could be done in practice.

KEY WORDSwelfare function, alternatives to GDP

CLASSIFICATIONJEL: D04, D63

PACS: 89.65.Gh


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PROBLEMS WITH THE UTILITY

The utility function, the central ingredient to micro-economics, can be understood as anabstract measure for happiness. Originally this happiness was considered to be an, at least in

principle, measurable quantity, but by the beginning of the 20th century economists hadconvinced themselves happiness is fundamentally subjective and evades any absolute scaling.Quantifying one persons levels of happiness (intrapersonal), and comparing different

persons levels of happiness (interpersonal) should thus be avoided because such efforts areeventually meaningless. Fortunately, in 1906, Pareto showed that an ordering of preferencesin good and not so good choices without an absolutely quantifiable measure is sufficientto reach an efficient equilibrium that maximizes happiness [1]. The absolute cardinal utilitywas thus replaced with the ordinal utility, and the concept of happiness by that of choiceor preference. Though in practice one often uses a particular quantification for the utility,this utility can be rescaled by an arbitrary monotonically increasing function.

While this shift from the cardinal to the ordinal utility has been advantageous by rendering

it unnecessary to deal with subjective quantities, the utility is a problematic concept forseveral reasons.

The most basic problem is one of interpretation. With the use of the utility, the pursuit ofhappiness was conjectured to be the fundamental driving force of our economies. Self-evident as that might sound, putting aside for a moment our personal strive for happiness andlooking at the evolution of civilizations, the idea that optimization of human happiness iswhat underlies the dynamics of this system does not make much sense. Being happy aboutones actions is not the driver of evolution, neither the biological nor the economical one. It

just happens that those who are happy about actions that also benefit the functionality of theirmetabolism have the advantage of desiring to do what helps them survive. Stil, what is

fundamentally important for natural selection is survival, not happiness. The deceptiveness ofhappiness becomes clear when we consider drugs that stimulate the brains reward system,

promising happiness on the expenses of early death.

However, it is unnecessary to attach any particular interpretation to the utility. In modelsbuilding upon it goods are utilized, but for no other purpose than to optimize the utility. Onemight thus postulate the utility as just some function that people happen to optimize in theirdecisions it is thus fundamentally a concept empty of meaning. And while this point ofview does away with the interpretational issue and is unproblematic from a mathematical

perspective, it is experimentally unfalsifiable and thus scientifically problematic. Without aninterpretation of the utility function independent of consumers actions, the question whetherconsumers do optimize their utility function can no longer be decided because it was postulatedwhatever they do is expression of that optimization already, and their behavior just revealstheir preferences (certain properties of the function however can be subject to experiment).

Another fundamental problem is that with ordinal utilities different consumers cannot becompared since it cannot be decided whether one persons happiness exceeds that of another.Though this seems reasonable, the problem it causes becomes clear with the second welfaretheorem. There are arbitrarily many states of our economy optimizing individual happinessthat differ in the distribution of wealth. If a distribution of wealth is particularly uneven, onedoes intuitively think of trying to increase happiness by redistributing from the rich to the

poor on the rationale that a rich man is less affected by the loss of $5 than a poor man by itsgain. Leaving aside the question how such a redistribution would be implemented, this

process would decrease the happiness of the rich, but increase that of the poor. However,since the utility of different consumers cannot be compared and therefore cannot be


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aggregated, there is no way to find out whether the increase in happiness outweighs thedecrease. There is thus no rationale for such an action based on the standard micro-economictheory. Only after defining a social welfare function that essentially provides a weight foreach consumer and thus allows to sum up or compare utilities becomes it possible to optimizesocial welfare. Exactly, what is optimized then depends in general on the definition of

social welfare underlying the so-defined function. The utilitarian (Benthamite) welfarefunction for example treats all consumers the same irrespective of their circumstances of living.

In contrast to this, a Max-Min (Rawlsian) welfare function is maximized when the utility ofthose consumers who have the least is the greatest. There are further various other functionsthat one can chose, each of which offers a different notion of aggregation and of socialwelfare. The use of the ordinal utility thus rendered the notion of social welfare ambiguousand made it impossible to satisfactorily tackle many important problems in welfare economics.

THE PURSUIT OF HAPPINESS

One might then ponder the question whether neuroscientific advances will eventually allow us

to indeed measure brain activity representing particular emotional states. Even if this becamepossible however, it is doubtful this would be meaningful for the economic purpose. Not only arethere many ways of happiness and a direct response to stimulus is only one sort, this approachalso raises the question what the relation between such brain activity and the economicrelevance of the brains owner should be. The idea that the ability of ones brain to reach highlevels of electrical or chemical activity means some consumers are more, some less receptiveto the unpleasantries of poverty is morally questionable and practically not very useful.

It thus remains the abstract notion of a preference map that is assumed to be existent butunknowable in principle, and only the used preferences are observable after they were actedupon. There are some few economists outside the mainstream who pursue the construction of

a cardinal utility for either interpersonal or intrapersonal comparisons, based on neurological,psychological or statistical measures, see e.g. [2-4] and references therein. The more widelyaccepted approach of New Welfare Economics measures peoples satisfaction with socialconditions by their willingness to pay, respectively accept, a monetary compensation forchange, relaxing Pareto-efficiency to Kaldor-Hicks-efficiency. However, also in this case acardinal measure for utility has to be used, thus the problem of aggregation remains.

The utility is thus an unsatisfactory basis for a model of our economy. One might instead takethe analogy to biology seriously and attempt to explain our economy as a direct continuationof natural selection, an approach pursued in the context of sociobiology. And though such areduction to more basic principles might theoretically be possible, our economic systemexhibits such complex features and such a plethora of emerging social and cultural propertiesit seems a very challenging task to derive a useful model in this way.

The question of quantifying happiness recently raised to renewed importance. Within the lastdecade, it has become widely acknowledged that the GDP is a poor measure for a nationswell-being, one of the main reason being that it leaves aside the happiness of the nationscitizens. There are thus many suggestions to replace or adjust the GDP with ameasure that

better represents the nations success, among others the Happy Planet Index1, the Index ofSustainable Economic Welfare, or the Genuine Progress Indicator (for a review on thesealternative measures, see [5]).

The awareness of the shortcomings of the GDP has meanwhile spread from academia topolitics. In 2008, French President Nicolas Sarkozy asked U.S. economist Joseph Stiglitz,winner of the 2001 Nobel prize in Economics and a critic of free market economists, and


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Armatya Sen of India, who won the 1998 Nobel prize for work on developing countries, foradvice on how to raise data more representative of his nations status. The French governmenthas since brought into life the Commission on the measurement of economic performance andsocial progress2to pursue this aim. In November 2010, British PrimeMinister David Cameronannounced his governments plans for measuring happiness [6], and it is not hard to predict

that other nations will follow these examples.

Such efforts to improve the GDP and deviate competition for its optimization to a measuremore indicative for well-being are overdue and welcome, but unfortunately do not solve the

previously discussed problems of quantifying and comparing different peoples happiness.Making use of surveys or similar means to obtain data is nothing but a specific procedure ofaggregation that attaches a chosen weight to everybodys state of mind, making it possible toadd the results together and arrive at a quantity for the whole nation. Intuitively, fairnessseems to demand to assign the same weight to every citizen. But as we have seen in the

previous section there is no scientific basis for this assignment. One might for example arguethat a persons suffering from environmental distress depends on their exposure and such on

their place of living, which should be reflected in the weighting of their (un-)happiness. Orconsider it was shown that the genetic ancestry of the majority of one nations citizens isresponsible for a generally higher contempt with their social status. Should we not then takethis into account when comparing the happiness of different nations? And if so, how?

We are thus back at the century-old problem of how to aggregate happiness.

POSSIBILITY VERSUS UTILITY

Considering the problems with aggregating happiness, we will here follow a differentapproach to address the question of societal well-being. We propose that the maximization ofutilities is not the fundamental driving force, neither of the individual, nor of our combined

social, political and economical systems, but that it is another quantity that is being optimized.The hypothesis is that what we work towards instead, both personally and collectively, isoptimizing possibilities. This quantity constitutes an utility function, thus leaving theapparatus of microeconomics functional as usual, but this utility function has the merit that itcan be aggregated, thus solving the previously discussed problems. We will further argue that

possibilities provide a substitute for happiness that is at least in principle objectively quantifiable.

Let us start then with asking a simple question: Why do we work to get rich? Money itself isnot of use, except possibly to paper the walls. As the saying goes, one cannot eat money.Money however promises safety, and it brings influence. It is not money itself that we desire,it is the possibilities it opens, whether we will eventually use them or not. What we aim toavoid is running out of possibilities, since lack of possibilities brings us in great risk of

becoming victim of changing circumstances that we cannot adapt to. Without possibilitiesthere is no change, without change there is no innovation, without innovation no progress.The whole power of capitalism stems from the allocation and investment of money to explorefurther possibilities. Heidegger described death as the possibility of impossibility of all

possibilities3, a phrase that seems equally apt also for bankruptcy.

This might serve as a motivation for why we will in the following consider maximizingpossibilities as the driving force for the dynamics of our economies. It should be understoodthis is a hypothesis, but one that we hope becomes plausible and whose usefulness becomesapparent in the following. Eventually however, it would need to be tested by contrasting itwith real world data. But first we need to lay out what the economy looks like.


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The economic system is described by a network withN nodes of agents, exchangingM goods.Agents, denoted FA, could be consumers or producers, households or companies. Goods areanything that can be exchanged between agents, including labor, money, services orinformation. Agents have each an inventory with entriesxAa(t), which is the amount of good aagent A has at time t in some agreed upon basis of units. The set of basis vectors containing

one item of a good span the space of goodsX, its zero vector will be denoted 0(goods that donot belong to anybody may be considered belonging to a dummy agent). We will neglect thatgoods might be perishable and thus strictly speaking should have a time dependence too, butthis could easily be incorporated in the framework.

The links of the network are described by a tensor EABa(t), where capital indices label agentsand run from 1 toN, and small indices label commodities and run from 1 to M. ThenEABa(t)is the amount of good a exchanged between agents A and B at time t. The entries can be

positive or negative valued, depending on whether a good was obtained or given away, it isthus4EABa = EABa. We will for convenience assume that exchanging goods happensinstantaneously. The time parameter itself is not necessarily related to any real clock, but just

what prevents everything from happening at once, as J. Wheeler put it. Time proceeds indiscrete steps with step size t. An agent FAwith no links connected to it will haveEAB(t) = 0for each B. We will call it inactive at time t. We will refer to a trade as being possible ifthe agent can reach agreement on it with an exchange partner. With a slight abuse of word,the trades encoded in EA do include non-exchange actions, such as giving a gift withoutreturn but, more importantly, connecting a good to a previously inactive node.

The network we are considering does not grow in the sense thatN andM do not change withtime. However, a good might not have been be produced or exchanged, or an agent mighthave been inactive before a time t0. The network itself is not necessarily simply connected atany time. These quantities are schematically depicted in Figure 1.

The nodes of the network are the agents with action functions FAthat act on input at time t toproduce output at time t + t

FA: X X, FA: )()( AA ttxtxoutin . (1)

These functions will generally be non-linear. They contain all the details about the individualagent, in particular his memory, expectations and future plans and thus the conditions underwhich it will agree on transactionsEAB. The actions of the agent encoded in this function willin general depend on what input he previously used (what goods consumed, what servicesused). The agent FAmight for example contain how well maintained a factorys machinery is,

Figure 1. The state of the economy at a moment in time. Depicted are links withnonvanishing exchange matrices. The agent FFis inactive.

FB,IB

FC,IC

FF,IF

FD,ID

FA,IA

FE,IE

ECB

ECD

EDB

EAB

EEB


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or what skills a worker has acquired over his lifetime. Any production process defines anetput vector

),()()( AA ttxFtxtxin

AA

innp . (2)

We will refer to two production plans as being different if their netput vectors differ. Thestate of the economy at time t is described by the set S(t) = {xA(t),EAB(t), W(t)}, where W(t)contains all external conditions of the world that are not already described by the network,such as for example the weather, the geological environment, or the political system. It alsocontains all externalities that might influence the agents actions but are not obtained by trade.The actions of agents in the network can be affected by and affect the external conditions.FA(t) andW(t) encode the dynamics of the system. While W(t) should in principle be given byan evolution law, in practice it will only be known probabilistically. Quantity FA(t) dependson the actions of the agent in each time step. We will use Sito refer to a specific initial stateat time ti.

The agents inventory updates according to

ttxFtEttxA

BAABA

),()()(

. (3)

saying that the inventory at time t + t is what was produced from the inventory at time tplusgoods obtained from trade. At each time step the agents decide what to do with theirinventory. The actions they can perform is producing output from input and/or connectinginventory to other nodes. They can connect to inactive nodes, which describes the creation ofa new process (or at least the attempt to do so). Agents do not necessarily have to use all oftheir inventory at one time step.

We can now define what we mean with the notion of possibilities. The total number of

possibilities of the network PS(t)at one time moment is the number of different actions theeconomys agents could take. More important than the possibilities at one moment in time is

the number of possible actions over a period of time. Since an agents actions affect that andothers agents inventory and the state of the economy, the possibilities at later times willdepend on the previous choices. Each time-ordered series of possible actions defines a historyof the economyH(Si, te). Each different action of any agent defines a branching of the pathsof the state of the economy. The total number of possible paths from Sito a final time tewewill denote #H(Si, te). It will in general depend on the external conditions W(t). Figure 2depicts a tree of such states.

Let us state the following hypothesis:

Hypothesis: Given an initial state Siand an endtime tethe economic system maximizes #H(Si, te).

The endtime tecould theoretically be infinite, but more realistically would be the time whenour economic system is no longer adequately described by the here proposed framework,either because of significant changes of the human species, our social systems, theenvironment, or a combination of those. While this is philosophically a troublesome time toset, we will see in the following that for practical purposes we need not fix this unknown timeanyway. In case #H was infinite, one further would have to deal with ratios of the number of

paths which would be an added complication but theoretically doable. However, this too willturn out not to be necessary in practice.

Maximization with a given initial condition does not necessarily mean an increase ofpossibilities with time. The initial conditions could result in a breakdown of the system withany possible course of action, such that even the optimal history results in a decrease of

possibilities. Note further that the quantity defined here does not leave interpretational


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Figure 2.Every path from tito teis a possible evolution of the state of the economy S. Dotsin this diagram correspond to states of the network as depicted in Figure 1.

questions open. It is not the possibilities for a particular purpose that are being counted, butjust all possibilities.

That is as far as the evolution of the system is concerned. One should understand this in asimilar sense to the working of natural selection that optimizes the survival chances of genes.While this might be the underlying trend of Nature as a whole, looking at the behavior of anindividual organism over a short period of time, an organism might do better or worse inreaching this goal. Consequently, the selective process in the whole system might proceedfaster or not so fast, and at any time we will be faced with some variety of species that

perform differently. Thus we have to ask now how the individual behavior supports thismaximization of possible histories.

For this purpose we define an agents possibilities in a state of the economy PAS(t)as thenumber of all possible actions that the agent could take with his inventory at this time. Forexample if the agent has 3 apples, 2 empty bottles and 5 bananas, he could trade 1 to 3 apples,1 or 2 bottles, and/or 1 to 5 bananas with whoever is willing to trade them. Or he couldconsume some apples or bananas, or make juice of some of the apples (both of which would

be a production process), or any combination of this. Then the space of possible actions is

)()()()(),()( txtxtxtxtxt AinAeAinAeAA , (4)

wheree

Ax is a possible trade for agent FA,in

Ax is the input of a possible production process,and the inequality is as usual meant to hold for every entry of the vector. This space isdegenerate since not all of the production processes might differ in their netput vector. Oncecould e.g. add input that is not used in a process altogether, but this should not count as anadditional possibility. Thus we formally mod out these options over the set of netput vectors

A/{np

Ax }, meaning we only count two elements of A as different possibilities if their

netput vector differs.

The number of possible actions of the agent is then the cardinality of that space

PAS(t)= #A/{np

Ax }.

Note that according to our definition of the exchange matrices, this space contains the actionsof connecting goods to a previously inactive node. That would correspond e.g. to the agent of

te

ti

Si


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putting his bananas on a pile and hoping for somebody to bring milk and a mixer. As before wethen see that the number of possibilities at one time is not a particularly insightful quantity. Thisspace is vast, but a lot of the possible actions will significantly decrease future possibilities (the

bananas may just rot away). More relevant is thus the number of possible future evolutions anaction opens. We define the space of all possible time-ordered sequences of actions from an

initial state to an endtime to beHA(Si, te). The number of possible paths is then #HA(Si, te).

An agents possibilities depend on his inventory, but they do also depend on the networkarchitecture and his location in it, and thus eventually also on the actions of the other agents.This, too, is similar to natural selection the agents performance depends on theenvironment that is also used and shaped by others. This then adds an additional uncertaintyto his optimization problem. If he assumes all other agents decide their actions using the samemodel as he does, their behavior is not uncertain, but in general this lack of knowledge aboutthe others behavior does enter the estimate of probabilities for different paths. What eachagent individually tries to achieve is a maximization of future possibilities. While this would

be an exact prescription if the evolution of the state of the world and the model agents use to

make decisions was known, in lack of this knowledge only probabilities for possibilities canbe given. Into the optimization then enters the agents willingness to take risk.

Before discussing the consequences of this setting, let us note that the number of possiblepaths (of an agent or of the economy itself) will grow in time just because choosing from afixed set options in each moment already allows for many different histories. If there are ndifferent choices, and this number remains constant over time, the number of possible paths

will grow with ttt ien /)( . A more useful quantity to characterize the growth of possibilities is

thus the natural logarithm of the number of histories Q(t): = lnPS(t), or for the single agent

QA(t): = ln PAS(t). If the time derivative of these quantities vanishes, the set of optionsremains constant.

Another important point is that an agent tries to maximize possible paths of actions for aparticular time period TA. This time period might be individually different and might or mightnot exceed the agents own lifetime. If it is a sharp cutoff, it corresponds to the BuxtonIndex [7]. More generally, if the agent instead considers short-term maximization morerelevant than longterm maximization he would discount the future in the usual way. ThoughTAtheoretically could be infinitely long, humans do not usually make plans for eternity. It isfor this reason that the endtime te is practically irrelevant since one would not expect it toenter any human considerations.

In their optimization process, agents are subject to biological, physiological, psychologicaland cognitive constraints. The first three represent constraints on what an agent can or will

agree to do, while the latter is a constraint on how well he can plan and judge.As far as the first three constraints are concerned, for example the survival of an agent is a

prerequisite for her further action and thus a top priority, and she will have to balance leisure-timewith work time to remain resilient and functional over a maximal time period. Agents mightfurther have a limited ability to adapt to changing conditions which constrains their coursesof actions and might result in self-limiting their actions to histories that evolve slow enoughto accommodate their needs5. These constraints are encoded in the agents functions FA, andwith them taken into account the outcome of the optimization might be lowered. Theconstraints might be expressed in the form that if #HA increases rapidly, or if there aresubstantial changes to the network structure, the productivity of the agent decreases.

Given these constraints on what the agent can and will do, it is thus not surprisingpossibilities are positively correlated with happiness, since well-being is in many cases


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beneficial for productivity and creativity. The difference between optimizing either wouldbecome apparent if it could be shown people sometimes chose to increase their possibilitiesrather than increasing their happiness. While in a slowly changing environment (slow incomparison to effects of natural selection to become relevant, i.e. at least some generations),

both should be well aligned with each other, in a fast changing environment happiness might

be optimal for choices that do no longer optimize possibilities since biological adaption hasnot caught up6. Agents also have finite cognitive abilities, meaning they will not be able toaccurately evaluate and judge all possibilities they have and thus will make mistakes. Anagent that performs very badly, e.g. by choosing an action that drastically limits his future

possibilities runs in great risk of becoming inactive, and in any case reduces his potential toinfluence the course of the economy. This is just because it is exactly those with few

possibilities who have few impact on future change. The economy will thus come to bedominated by agents that perform well in optimizing their possibilities7.

The number of an agents possibilities for taking a particular action represents a utilityfunction of that agent. As we noted earlier, for micro-economics it is irrelevant exactly what

the function to be optimized describes. In contrast to the usual case however, the number ofpossibilities is an absolute number that also allows for intra- and interpersonal comparisons.

Let us then discuss how the individual level connects to the collective level.

WELFARE ECONOMICS

Merely looking at individual actions, the total number of possibilities for the whole economicsystem is not automatically maximized. Consider for example a network structure describinga free market. In this situation, we know that the individual actions will work towards Paretoefficiency. The number of possibilities however is an aggregated measure not taken intoaccount in this efficiency. There could thus be trades that do decrease the possibilities of some

agents, but do increase the possibilities of a larger group of agents, leading to an overall increase.At this point it becomes relevant that our economic systems are always complemented bysocial and political systems. The social and political context is commonly treated as externalto the economic system, providing rules, regulations and norms, which we previouslyencoded in the function W(t). However, we should actually be interested in the combineddynamics of the whole, since social values, politics and economics have a non-negligibleinteraction and neither of them can strictly speaking be considered independently. Theirseparation is an additional assumption that will not in general be fulfilled. Then, for thequestion of collective optimization, the optimization should be one of all these systemscombined. In this case, the function W(t), that we previously considered as externally given,is a function of the variables of the economy, and the central hypothesis is that in this case theoptimization includes W(t). Treating the political and social environment as external ishowever often justified since one might argue that the political process operates more slowlythan that of the economy and social norms and values change even more slowly. The questionof social welfare we want to address in this section then concerns the combination of politicalenvironment and the economy.

The central hypothesis offered here is, again, that we work towards maximizing our totalpossibilities. Pareto efficiency alone is then not necessarily optimal and thus our economicsystems are not entirely free markets but complemented by laws, regulations, and taxessupposed to complete the task of optimization the economy does not already fulfill. This then

provides a rationale for many governmental public services that lack a justification if one

believes in the free market paradigm: a good education opens future possibilities; retirementoptions ensure we do not run out of possibilities when we age; social and health insurance are


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supposed to lower the risk of early death. Even the political system itself can be more or lesshelpful to this end of optimizing possibilities. Democracy is based on personal freedom, and

providing a social and political environment supportive of upwards mobility is the essence ofmaximizing everybodys possibilities.

Human beings further naturally have an interest in ensuring the survival of their offspring.Many of us work hard to make the world a better place for future generations. The relevanceof improving our lives and the lives of those to come is a motivation for constant innovationand improvement, and not spoiling the possibilities of future generations is what underlies theenvironmental movement, captured in the proverb We do not inherit the Earth from our

parents, we borrow it from our children, reminding us of our responsibilities.

Environmental protection is often origin of heated argumentation because we frequently usefor our present well-being resources that might no longer be available in the future.Employing the utility function we would wonder how much more important our happinessnow is compared to that of coming generations. As previously discussed, even neglecting ourlimited ability to predict the future, such a comparison is impossible since different agents

happiness stand in no absolute relation to each other. Similarly, whether or not people wereless happy some centuries ago because their lives were on the average shorter and offeredfewer possibilities is a question we will probably never be able to answer.

But with the above outlined framework we can now rephrase this discussion. Doesvoluntarily reducing growth now and thus giving up possible histories in the short-term, orcausing a reduction of possibilities in the future and giving up branches in the long-term,amounts eventually, with some probability, to more or less total possibilities? And while thisreformulation still contains the problem of estimating the evolution of the system and ischallenged by the inaccuracy of our predictions, it does no longer entail the necessity ofcomparing agents ordinal utilities.

The case is similar with uneven distributions of wealth displaying a gap between rich and thepoor. While a comparison between a rich mans and a poor mans utility for $5000 cannot bedone, the increase or decrease of future possibilities opened with this check can be compared.Providing a family in a developing country with basic immunizations and a mosquito net canvastly increase their future possibilities, while giving up the amount of money needed for thisin a developed country might hardly decrease the number of possibilities.

As before when comparing the now with the then, this comparison between the here and thethere does still depend on our ability to estimate future evolution, but it got rid of the problemwith relating different peoples utilities. Of course the question what action increases the totalnumber of possibilities is infinitely more involved than the brief examples above.

Redistributing wealth causes disincentives for work, which might eventually reducepossibilities even further. There also remain the questions of value, for example what amountof reducing somebodys possibilities to increase the total possibilities is considered fair, as aredistribution considered unfair may lead to political frustration and eventually also decreaserather than increase possibilities. The point here is not to make any claims what particularaction is beneficial for social welfare, but that the quantification of possibilities is a usefultool to characterize the impact of planned actions. How many possibilities is one countrywilling to give up to increase the possibilities of another country? How much risk should weexport on future generations? These are questions that only political process can decide. Whatwe can do however is to provide a measure for the impact of such decisions.


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DISCUSSION AND SUMMARRY

We have here proposed that individuals strive to optimize the number of future possibilitiesand that our political systems are tools to collectively improve on the total number of

possibilities of a group or nation. Of course these tools are imperfect. Like individual human

action, the realized political environment can work better or worse towards the maximizationof total possibilities since we might be lacking information, understanding, or just makewrong decisions. Much like the efficiency of our economic system has benefitted from a(partial) theoretical understanding of its models, the function of our combined economicaland political system might benefit from understanding the here proposed model.

It is however not necessary to believe the hypothesis proposed here to find the number ofpossibilities a useful quantity: The number of possibilities provides a substitute for theethereal notion of happiness and thus makes a scientifically sound aggregation possible.While we have here not constructed explicit examples, it is in principle a quantifiablemeasure. For practical purposes, one would of course have to make simplifying assumptions.

Consider one would like to quantify the possibilities of two families in two different nationsfor comparison. First, one would chose a suitable time-step, say, one month, and a suitabletime period over which to trace histories, say, four years. Then, one would have to agree onwhat aspects of life to consider access to goods, education, public and private services,health care, etc and itemize them or assign to them suitable amounts, each constituting a

possible, discrete, choice. In addition, one might consider a number of representativecontingencies of interest that might happen with some probability, for example a dry summeror illness of a family member. After this, one could compute what possible combinations ofchoices the person can make with their monthly income. Lacking health care for examplemight mean for a family with a sick child that their possibilities are drastically reduced.Lacking access to transportation might reduce the access to education or medical help, both

resulting in a lowered number of future possibilities. The selection of goods reflects thegeneral infrastructure and status of the economy, while the job opportunities affect thefamilies possibilities through the monthly available money to spend.

Of course the so constructed measure would only be an approximate indicator of the truenumber of possibilities and depend on the selection of histories considered, but with suitablechoices it could provide a good impression of a nations well-being.

One can devise tests for the here proposed hypothesis along the same lines. To that end, oneneeds to study situations where people, besides engaging in economic exchange, havecollective decision making processes that supplement the free market mechanism. Whilemost democracies are of that sort, for practical purposes a smaller system would be preferable.

A real-life example may be agricultural communities in developing countries, or possiblysome game can be devised which simulates a suitable setup. One then needs again aquantification and discretization of possibilities as outlined in the previous paragraph. Thequestion to test is whether people collectively strive to a situation where, given sufficientinformation, the aggregated number of possibilities for all of them is maximized.

In summary, we have proposed here that the dynamics of our combined economic andpolitical systems work towards optimizing the number of possibilities. Considering only theeconomy, the number of possibilities constitutes a cardinal utility function that allows intra-and interpersonal comparison, and thus makes aggregation possible. This aggregation resultsin an additional measure whose optimization cannot be achieved within the economy alone,

thus providing a rationale for politically pursued social welfare. We have further outlined


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how the number of possibilities can in practice be calculated by selecting representativegoods, public and private services, as well as contingencies. In this manner, it may provide ameasure supplementary to the GDP.

ACKNOWLEDGMENTS

I thank Arun Gupta, Kelly John Rose, Stefan Scherer, Lee Smolin and Samuel Vasquez forhelpful discussions.

REMARKS1http://www.happyplanetindex.org.2http://www.stiglitz-sen-fitoussi.fr/en.3Die Mglichkeit der Unmglichkeit aller Mglichkeiten.4In an economy with fiat money, most of the exchange will happen via one particular good4that counts this money. While the exchange matrix then will remain mostly empty, this case4is also covered by the outlined framework.5

Irvin Yalom lists freedom as one of the four existential fears, since being faced with too5many choices can greatly increase the anxiety to make irreversible mistakes. Some religious5sects refuse making use of medical or technological achievements of our modern 5civilizations5(one might say though with the attempt to increase possibilities in afterlife). These are only5two examples of how psychological constraints might result in self-limiting ones possibilities.6A large number of people in the Western world nowadays suffers from permanent stress in6reaction to the demands of their every-day life. This biological stress reaction is arguably a6relic of evolution that is in most cases no longer beneficial in the modern world. One may6ponder the question then if not the holding-on to a stressful lifestyle is an expression of6optimizing possibilities rather than happiness.7At least over their own lifetime. Increasing ones lifespan or immortality could result in a

7dramatic increase of individual possibilities. It is thus unsurprisingly a goal that is vigorously7pursued.

REFERENCES[1] Pareto, V.:Manual of Political Economy. In Italian.

M. Kelley Publishers, 1971,

[2] Van Praag, B.M.S.: Ordinal and Cardinal Utility: An Integration of the Two Dimensionsof the Welfare Concept.Journal of Econometrics 50(1-2), 69-89, 1991,http://dx.doi.org/10.1016/0304-4076(91)90090-Z,

[3] Ng, Y.-K.: A Case for Happiness, Cardinalism, and Interpersonal Comparability.Economic Journal 107(445), 1848-1858, 1997,http://dx.doi.org/10.1111/j.1468-0297.1997.tb00087.x,

[4] Kornienko, T.:A Cognitive Basis for Cardinal Utility.https://docs.google.com/file/d/0B8TX9abA2uy0ZjNFR2V1eWFndXc/edit?pli=1, accessed 3 October 2010,

[5] Goossens, Y. et al.:Alternative progress indicators to Gross Domestic Product (GDP) asa means towards sustainable development.Study IP/A/ENVI/ST/2007-10, European Parliament, 2007,http://www.beyond-gdp.eu/download/bgdp-bp-goossens.pdf, accessed 6 July 2009,

[6] Castle, T.: U.K. to measure happiness alongside GDP.Globe and Mail, 25 November 2010,

[7] Dijkstra, E.W.: Selected Writings on Computing: A Personal Perspective.Springer-Verlag, New York, 1982,http://dx.doi.org/10.1007/978-1-4612-5695-3.


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O PROBLEMU MJERENJA SREE

Sabine HossenfelderNORDITAtokholm, vedska

SAETAKPitanje kako mjeriti i prikupljati sreu starije je od stoljea. Zadnjih godina njegovo je znaenje poraslo zbogtenji da se BDP zamijeni indeksom koji bi bolje indicirao blagostanje, iako su takve tenje povezane sozbiljnim konceptualnim problemima. Nakon kraeg navoenja tih problema predlae se da im se pristupi,umjesto uobiajenom ordinalnom korisnou, alternativnom veliinom koja je maksimizirana u ekonomskimtransakcijama. Ta veliina broji budue mogunosti koje se otvaraju zahvaljujui robi. Velika prednost ovog

pristupa je to to je, u principu, broj mogunosti objektivna mjera koja omoguuje individualnu usporedbu iliusporedbe vie osoba. Postavljen je okvir modela i prodiskutirano njegovo znaenje za drutveno blagostanje. Uradu nije izravno izraunata mjera kojom bi se zamijenio BDP nego je naznaeno kako bi se to provelo.

KLJUNE RIJEI

funkcija blagostanja, alternativa za BDP

Documents

Hossenfelder. on the Problem of Measuring Happiness